I agree. I would also go further and refuse to answer any more of her queries, because answering her is obviously pointless. It might teach her not to ask questions in future if she's not going to pay attention to the answers.

This. Personally I think it is unacceptable for one adult to say 'shush' to another, especially in a profession a setting. I would say this to her every single time she said 'shush' to me, no matter what the question was.

MissRose:
If this person keeps this up, it could go into PD territory. Honestly, here is how I would handle it:

Co-worker: I need this setup done to do my job

Me: Just a few moments please, let me go into the systems for you to do what is needed.

Co-worker: Shush, I can go to IT directly to do it faster

Me: I can get it done now, or if you submit an IT ticket to the help desk group per office procedure, the request takes much longer. Do you wish to wait a 1/2 day at least or not?